At the Intersection of Money and Reform Part III: On Cost Functions & the Increased Costs of Higher Outcomes
In my 2012 report Does Money Matter in Education, I addressed the education production functionliterature that seeks to establish a direct link between resources spent on schools and districts, and outcomes achieved by students. Production function studies include studies of how variation in resources across schools and settings is associated with variations in outcomes across those settings, and whether changes in resources lead to changes in the level or distribution of outcomes.
The Education Cost Function
The education cost function is the conceptual flip side of the education production function. Like production function research, cost function research seeks to identify the link between spending variation and outcome variation, cross-sectionally and longitudinally. The goal of the education cost function is to discern the levels of spending associated with efficiently producing specific outcome levels (the “cost” per se) across varied geographic contexts and schools serving varied student populations. Most published studies applying cost function methodology use multiple years of district-level data, within a specific state context, and focus on the relationship between cross-district (over time) variations in spending and outcome levels, considering student characteristics, contextual characteristics such as economies of scale, and labor cost variation. Districts are the unit of analysis because they are the governing unit charged with producing outcomes, raising and receiving the revenues, and allocating the financial and human resources for doing so. Some cost function studies evaluate whether varied expenditures are associated with varied levels of outcomes, all else being equal, while other cost function studies evaluate whether varied expenditures are associated with varied growth in outcomes.
The existing body of cost function research has produced the following (in some cases obvious) findings:
- The per-pupil costs of achieving higher-outcome goals tend to be higher, across the board, than the costs of achieving lower-outcome goals, all else being equal.[1]
- The per-pupil costs of achieving any given level of outcomes are particularly sensitive to student population characteristics. In particular, as concentrated poverty increases, the costs of achieving any given level of outcomes increase significantly.[2]
- The per-pupil costs of achieving any given level of outcomes are sensitive to district structural characteristics, most notably, economies of scale.[3]
Researchers have found cost functions of particular value for evaluating the different costs of achieving specific outcome goals across settings and children. In a review of cost analysis methods in education, Downes (2004) explains: “Given the econometric advances of the last decade, the cost-function approach is the most likely to give accurate estimates of the within-state variation in the spending needed to attain the state’s chosen standard, if the data are available and of a high quality” (p. 9).[4]
Addressing the critics
This body of literature also has its detractors, including, most notably, Robert Costrell, Eric Hanushek and Susanna Loeb (CHL), who, in a 2008 article, assert that cost functions are invalid for estimating costs associated with specific outcome levels. They assert that one cannot possibly identify the At the Intersection of Money and Reform Part III: On Cost Functions & the Increased Costs of Higher Outcomes | School Finance 101:
